%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM687^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:18:32 AM UTC 2026
% Result : Theorem 0.08s 0.20s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 70 ( 23 unt; 0 typ; 7 def)
% Number of atoms : 259 ( 81 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 370 ( 59 ~; 47 |; 0 &; 244 @)
% ( 4 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 13 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 62 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x: nat ).
thf(func_def_1,type,
y: nat ).
thf(func_def_2,type,
z: nat ).
thf(func_def_3,type,
u: nat ).
thf(func_def_4,type,
more: nat > nat > $o ).
thf(func_def_6,type,
pl: nat > nat > nat ).
thf(func_def_9,type,
sF0: nat ).
thf(func_def_10,type,
sF1: nat ).
thf(func_def_11,type,
sF2: $o ).
thf(f1,axiom,
( ~ ( more @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(f2,axiom,
more @ z @ u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).
thf(f4,axiom,
! [X1: nat,X2: nat,X3: nat,X0: nat] :
( ( X0 = X1 )
=> ( ( more @ X2 @ X3 )
=> ( more @ ( pl @ X0 @ X2 ) @ ( pl @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19g) ).
thf(f5,axiom,
! [X2: nat,X1: nat,X3: nat,X0: nat] :
( ( more @ X0 @ X1 )
=> ( ( more @ X2 @ X3 )
=> ( more @ ( pl @ X0 @ X2 ) @ ( pl @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz21) ).
thf(f6,conjecture,
more @ ( pl @ x @ z ) @ ( pl @ y @ u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz22a) ).
thf(f7,negated_conjecture,
~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
more @ z @ u,
inference(rectify,[],[f2]) ).
thf(f9,plain,
( ( more @ z @ u )
= $true ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( X0 = X3 )
=> ( ( more @ X1 @ X2 )
=> ( more @ ( pl @ X3 @ X1 ) @ ( pl @ X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f11,plain,
! [X3: nat,X1: nat,X0: nat,X2: nat] :
( ( X0 = X3 )
=> ( ( ( more @ X1 @ X2 )
= $true )
=> ( $true
= ( more @ ( pl @ X3 @ X1 ) @ ( pl @ X0 @ X2 ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( more @ X3 @ X1 )
=> ( ( more @ X0 @ X2 )
=> ( more @ ( pl @ X3 @ X0 ) @ ( pl @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f13,plain,
! [X0: nat,X1: nat,X3: nat,X2: nat] :
( ( $true
= ( more @ X3 @ X1 ) )
=> ( ( $true
= ( more @ X0 @ X2 ) )
=> ( $true
= ( more @ ( pl @ X3 @ X0 ) @ ( pl @ X1 @ X2 ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ),
inference(rectify,[],[f7]) ).
thf(f15,plain,
( ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
!= $true ),
inference(fool_elimination,[],[f14]) ).
thf(f18,plain,
( ~ ( more @ x @ y )
=> ( x = y ) ),
inference(rectify,[],[f1]) ).
thf(f19,plain,
( ( ( more @ x @ y )
!= $true )
=> ( x = y ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
!= $true ),
inference(flattening,[],[f15]) ).
thf(f22,plain,
( ( ( more @ x @ y )
!= $true )
=> ( x = y ) ),
inference(flattening,[],[f19]) ).
thf(f24,plain,
! [X3: nat,X1: nat,X0: nat,X2: nat] :
( ( $true
= ( more @ ( pl @ X3 @ X1 ) @ ( pl @ X0 @ X2 ) ) )
| ( ( more @ X1 @ X2 )
!= $true )
| ( X0 != X3 ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f25,plain,
! [X1: nat,X3: nat,X0: nat,X2: nat] :
( ( $true
= ( more @ ( pl @ X3 @ X1 ) @ ( pl @ X0 @ X2 ) ) )
| ( X0 != X3 )
| ( ( more @ X1 @ X2 )
!= $true ) ),
inference(flattening,[],[f24]) ).
thf(f26,plain,
( ( ( more @ x @ y )
= $true )
| ( x = y ) ),
inference(ennf_transformation,[],[f22]) ).
thf(f27,plain,
! [X0: nat,X1: nat,X3: nat,X2: nat] :
( ( $true
= ( more @ ( pl @ X3 @ X0 ) @ ( pl @ X1 @ X2 ) ) )
| ( $true
!= ( more @ X0 @ X2 ) )
| ( $true
!= ( more @ X3 @ X1 ) ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f28,plain,
! [X3: nat,X2: nat,X0: nat,X1: nat] :
( ( $true
!= ( more @ X3 @ X1 ) )
| ( $true
!= ( more @ X0 @ X2 ) )
| ( $true
= ( more @ ( pl @ X3 @ X0 ) @ ( pl @ X1 @ X2 ) ) ) ),
inference(flattening,[],[f27]) ).
thf(f29,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true
= ( more @ ( pl @ X1 @ X0 ) @ ( pl @ X2 @ X3 ) ) )
| ( X1 != X2 )
| ( ( more @ X0 @ X3 )
!= $true ) ),
inference(rectify,[],[f25]) ).
thf(f30,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( ( more @ X0 @ X3 )
!= $true )
| ( $true
!= ( more @ X2 @ X1 ) )
| ( $true
= ( more @ ( pl @ X0 @ X2 ) @ ( pl @ X3 @ X1 ) ) ) ),
inference(rectify,[],[f28]) ).
thf(f31,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true
= ( more @ ( pl @ X1 @ X0 ) @ ( pl @ X2 @ X3 ) ) )
| ( X1 != X2 )
| ( ( more @ X0 @ X3 )
!= $true ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f33,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true
= ( more @ ( pl @ X0 @ X2 ) @ ( pl @ X3 @ X1 ) ) )
| ( $true
!= ( more @ X2 @ X1 ) )
| ( ( more @ X0 @ X3 )
!= $true ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f34,plain,
( ( more @ z @ u )
= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f35,plain,
( ( ( more @ x @ y )
= $true )
| ( x = y ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f36,plain,
( ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
!= $true ),
inference(cnf_transformation,[],[f20]) ).
thf(f39,plain,
! [X2: nat,X3: nat,X0: nat] :
( ( $true
= ( more @ ( pl @ X2 @ X0 ) @ ( pl @ X2 @ X3 ) ) )
| ( ( more @ X0 @ X3 )
!= $true ) ),
inference(equality_resolution,[],[f31]) ).
thf(f41,definition,
( sF0
= ( pl @ x @ z ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f42,plain,
( ( pl @ x @ z )
= sF0 ),
inference(reorient_equations,[],[f41]) ).
thf(f43,definition,
( sF1
= ( pl @ y @ u ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f44,plain,
( ( pl @ y @ u )
= sF1 ),
inference(reorient_equations,[],[f43]) ).
thf(f45,definition,
( sF2
= ( more @ sF0 @ sF1 ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f46,plain,
sF2 != $true,
inference(definition_folding,[],[f36,f45,f44,f42]) ).
thf(f47,plain,
( ( sF2 = $true )
| ( ( more @ sF0 @ sF1 )
= $false ) ),
inference(iff_proxy_clausification,[],[f45]) ).
thf(f50,definition,
( spl3_1
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f52,plain,
( ( x = y )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f50]) ).
thf(f54,definition,
( spl3_2
<=> ( ( more @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f57,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f35,f54,f50]) ).
thf(f68,definition,
( spl3_5
<=> ( sF2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
thf(f72,definition,
( spl3_6
<=> ( ( more @ sF0 @ sF1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
thf(f74,plain,
( ( ( more @ sF0 @ sF1 )
= $false )
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f72]) ).
thf(f75,plain,
( spl3_5
| spl3_6 ),
inference(avatar_split_clause,[],[f47,f72,f68]) ).
thf(f76,plain,
~ spl3_5,
inference(avatar_split_clause,[],[f46,f68]) ).
thf(f90,plain,
! [X0: nat] :
( ( $true
= ( more @ ( pl @ y @ X0 ) @ sF1 ) )
| ( ( more @ X0 @ u )
!= $true ) ),
inference(constrained_superposition,[],[f39,f44]) ).
thf(f126,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( more @ ( pl @ X0 @ X1 ) @ sF1 ) )
| ( $true
!= ( more @ X0 @ y ) )
| ( ( more @ X1 @ u )
!= $true ) ),
inference(constrained_superposition,[],[f33,f44]) ).
thf(f149,plain,
( ( ( more @ sF0 @ sF1 )
= $true )
| ( ( more @ z @ u )
!= $true )
| ( ( more @ x @ y )
!= $true ) ),
inference(constrained_superposition,[],[f126,f42]) ).
thf(f151,plain,
( ( ( more @ sF0 @ sF1 )
= $true )
| ( ( more @ x @ y )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f149,f34]) ).
thf(f156,plain,
( ( $false = $true )
| ( ( more @ x @ y )
!= $true )
| ~ spl3_6 ),
inference(forward_demodulation,[],[f151,f74]) ).
thf(f157,plain,
( ( ( more @ x @ y )
!= $true )
| ~ spl3_6 ),
inference(trivial_inequality_removal,[],[f156]) ).
thf(f158,plain,
( ~ spl3_2
| ~ spl3_6 ),
inference(avatar_split_clause,[],[f157,f72,f54]) ).
thf(f161,plain,
( ( ( pl @ y @ z )
= sF0 )
| ~ spl3_1 ),
inference(constrained_superposition,[],[f42,f52]) ).
thf(f166,plain,
( ( ( more @ sF0 @ sF1 )
= $true )
| ( ( more @ z @ u )
!= $true )
| ~ spl3_1 ),
inference(constrained_superposition,[],[f90,f161]) ).
thf(f173,plain,
( ( ( more @ sF0 @ sF1 )
= $true )
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f166,f34]) ).
thf(f174,plain,
( ( $false = $true )
| ~ spl3_1
| ~ spl3_6 ),
inference(forward_demodulation,[],[f173,f74]) ).
thf(f175,plain,
( $false
| ~ spl3_1
| ~ spl3_6 ),
inference(trivial_inequality_removal,[],[f174]) ).
thf(f176,plain,
( ~ spl3_1
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[],[f175]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f57]) ).
cnf(s3,plain,
( spl3_5
| spl3_6 ),
inference(sat_conversion,[],[f75]) ).
cnf(s4,plain,
~ spl3_5,
inference(sat_conversion,[],[f76]) ).
cnf(s9,plain,
( ~ spl3_2
| ~ spl3_6 ),
inference(sat_conversion,[],[f158]) ).
cnf(s10,plain,
( ~ spl3_1
| ~ spl3_6 ),
inference(sat_conversion,[],[f176]) ).
cnf(s11,plain,
spl3_6,
inference(rat,[],[s3,s4]) ).
cnf(s12,plain,
~ spl3_1,
inference(rat,[],[s10,s11]) ).
cnf(s13,plain,
~ spl3_2,
inference(rat,[],[s9,s11]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s1,s13,s12]) ).
thf(f177,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM687^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.14 % Computer : n012.cluster.edu
% 0.08/0.14 % Model : x86_64 x86_64
% 0.08/0.14 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.14 % Memory : 8046.5625MB
% 0.08/0.14 % OS : Linux 6.8.0-71-generic
% 0.08/0.14 % CPULimit : 300
% 0.08/0.14 % WCLimit : 300
% 0.08/0.14 % DateTime : Tue Sep 29 12:37:33 UTC 2026
% 0.08/0.14 % CPUTime :
% 0.08/0.14 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 Running higher-order theorem proving
% 0.08/0.18 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.20 % (43928)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.20 % (43939)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.08/0.20 % (43939)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.08/0.20 % (43939)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1882885836:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_3000 on theBenchmark for (3000ds/157Mi)
% 0.08/0.20 % (43939) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-43928-43939"...
% 0.08/0.20 % (43939)...printing done.
% 0.08/0.20 % (43933)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1461884553:s2a=on:i=87:rtra=on:ntd=on_3000 on theBenchmark for (3000ds/87Mi)
% 0.08/0.20 % (43934)lrs+10_16_si=on:nwc=1.5:random_seed=1110549849:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_3000 on theBenchmark for (3000ds/18Mi)
% 0.08/0.20 % (43935)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=737847716:i=3:rtra=on:inj=on:ntd=on_3000 on theBenchmark for (3000ds/3Mi)
% 0.08/0.20 % (43937)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4128198513:i=24:av=off:rtra=on_3000 on theBenchmark for (3000ds/24Mi)
% 0.08/0.20 % (43936)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3552936497:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_3000 on theBenchmark for (3000ds/634Mi)
% 0.08/0.20 % (43938)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1217538398:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_3000 on theBenchmark for (3000ds/75Mi)
% 0.08/0.20 % (43939)Refutation found. Thanks to Tanya!
% 0.08/0.20 % SZS status Theorem for theBenchmark
% 0.08/0.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.20 % (43939)------------------------------
% 0.08/0.20 % (43939)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.20 % (43939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.20 % (43939)CaDiCaL version: 2.1.3
% 0.08/0.20 % (43939)Termination reason: Refutation
% 0.08/0.20 % (43939)Time elapsed: 0.004 s
% 0.08/0.20 % (43939)Peak memory usage: 13 MB
% 0.08/0.20 % (43939)Instructions burned: 10 (million)
% 0.08/0.20 % (43928)Success in time 0.019 s
% 0.08/0.20 % Vampire exiting
%------------------------------------------------------------------------------